Does the ultimatum game contradict game theory?
One of my favorite parts of class is when we talk about games–especially the games that reveal something fundamental about human behavior. The first game we encountered like this was the prisoner’s dilemma. We learned about the prisoner’s dilemma when we were first learning about game theory. The fundamental idea behind game theory is making a decision maximizing your own payoff while considering what the other player will do, also.
More recently, we’ve learned about the ultimatum game. In the ultimatum game, one person (the giver) is given any amount of money to distribute between themselves and one other person (the receiver). The receiver can then either accept or reject that amount, and if the receiver rejects that amount, then the giver does not get anything either. So the game that the giver is playing is to estimate the smallest amount possible to give the receiver, so that the receiver will not reject the offer, and that the giver will be maximizing his payoff.
If this was what actually happened the majority of the time in the ultimatum game, this would fit right in with the game theoretic model that we have been learning about, because it is literally a game about making the best decision possible for yourself while considering how the other person would react and affect the outcomes.
But in reality, the ultimatum game at face value does not seem to align with that framework. For one thing, receivers should theoretically be willing to accept any amount above 0, because they will be better off than they were before that got even an incremental amount of money. But when you run the experiment, you actually find that “approximately half of the receivers turned down offers under 30 percent” (http://money.howstuffworks.com/ultimatum-game1.htm). Additionally, the average offer in experiments ranges from 37% to even 50% of the money (still http://money.howstuffworks.com/ultimatum-game1.htm).
The givers giving anywhere from about 37-50% can be explained by game theory pretty well. If the giver suspects that the receiver will reject something that is too low, the giver will offer more than we might expect, but why would a receiver ever reject an offer above 0? Half of the receivers rejecting offers below 30% of the money seems, at least to me, a pretty large number of people turning down money with no strings attached. Especially when you consider that game theory is about maximizing payoff. If you are a receiver, and you know that your only options are accept money or reject money (assuming that the giver offers you a value above 0), then accept money would be a dominant strategy to maximize your payoff.
However, in game theory you must analyze the entire payoff of a decision in a game–and this includes emotional payoff! In the ultimatum game, perhaps the receiver finds an offer below 30% of the money to be so insulting that it is more worthwhile to deny the giver their part of the money rather than accept a grossly low amount. After all, every split below 50% means that the giver has more to lose than the receiver has to gain monetarily, and so if the emotional satisfaction of denying the giver their part is equivalent to the amount of money they would have gotten, then the receiver really will have a better payoff by doing that. Alternatively, rejecting an offer that is seen as too low could be used as a way to maintain a sense of self-worth and the idea that you are a person with standards, which also may be more worthwhile than a monetary value, depending on the person.
Another interesting game to consider, which I read about in the article I am linking, is the dictator game. In this game, the giver has some money to split between themselves and another person. But this time, no matter whether the receiver accepts the money or rejects it, the giver gets to keep the money. One catch: the only splits that are options are $2/$18 and $10/$10. In this case, we might expect that the givers are definitely only giving the receiver $2 and keeping the rest for themselves, but actually, 67% of givers decided to split the money evenly. What! Why?
A slightly different version of the dictator game may shed some light on this issue. The only difference between this one and the one described above is that there are two rounds in this game. In the first round, Person 1 is the giver and Person 2 is the receiver. In the second round, Person 2 is the giver and Person 1 is the receiver. It was found that the outcome of the second round correlated very strongly with the outcome of the first round. So, if the giver split the money evenly, the receiver would be more likely to split the money evenly in the next round. And if the giver chose the $2/$18 split, the receiver would be more likely to choose that split as well.
For me, the results of the dictator game show that people are taking a lot more than immediate situations into account when making decisions. If you only expected your one decision to affect the immediate situation, you would always choose the most selfish option. But that’s not how we see life working. People have memories, and take past events into consideration, as evidenced by the second round of the dictator game. And people know that one day they could be the person without the power–and in a situation more serious than this game. Perhaps being more fair is a strategy that minimizes the risk of others doing harm to you, and thereby a strategy that maximizes payoff, considering multiple factors over a period of time? If true, this is an argument for the ultimatum game (and dictator game) fitting into our game theory models.
Sources:
Class lectures & textbook
http://money.howstuffworks.com/ultimatum-game.htm